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(1)

1

Apparent efficiency of serially coupled columns in isocratic and gradient elution

1

modes

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3

AUTHORS: Szabolcs FEKETE1*, Santiago CODESIDO1, Serge RUDAZ1, Davy

4

GUILLARME1, Krisztián HORVÁTH2

5

6

1 School of Pharmaceutical Sciences, University of Geneva, University of Lausanne, CMU -

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Rue Michel Servet, 1, 1211 Geneva 4 – Switzerland

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2 Department of Analytical Chemistry, University of Pannonia, Egyetem u. 10, 8200

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Veszprém, Hungary

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CORRESPONDENCE: Szabolcs FEKETE

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Phone: +41 22 379 63 34

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E-mail: szabolcs.fekete@unige.ch

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*Manuscript

Click here to view linked References

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Apparent efficiency of serially coupled columns in isocratic and gradient elution

15

modes

16

17

Abstract

18

The goal of this work was to understand the variation of apparent efficiency when serially

19

coupling columns with identical stationary phase chemistries, but with differences in their

20

kinetic performance. For this purpose, a mathematical treatment was developed both for

21

isocratic and gradient modes to assess the change in plate numbers and peak widths when

22

coupling arbitrary several columns. To validate the theory, experiments were also carried out

23

using various mixtures of compounds, on columns packed with different particle sizes, to

24

mimic highly efficient (new, not used) and poorly efficient columns (used one with many

25

injections). Excellent agreement was found between measured and calculated peak widths.

26

The average error in prediction was about 5 % (which may be explained by the additional

27

volume of the coupling tubes).

28

In isocratic mode, the plate numbers are not additive when the coupled columns possess

29

different efficiencies, and a limiting plate count value can be calculated depending on the

30

efficiency and length of the individual columns. Theoretical efficiency limit can also be

31

determined assuming one column in the row with infinite efficiency.

32

In gradient elution mode, the columns’ order has a role (non-symmetrical system). When the

33

last column has high enough efficiency, the gradient band compression effect may

34

outperform the competing band broadening caused by dispersive and diffusive processes

35

(peak sharpening). Therefore, in gradient mode, the columns should generally be

36

sequentially placed according to their increasing efficiency.

37 38

Keywords:

39

Column coupling, apparent efficiency, plate number, peak capacity, column length

40

41

(3)

3

1. Introduction

42

The idea of coupling columns to analyze complex samples appeared quite early in

43

chromatography [1,2,3,4,5,6]. The purpose of column coupling can be either to improve

44

kinetic performance by increasing the column length or adjust selectivity by combining

45

different stationary phase chemistries. This latter idea lead to the development of

46

multidimensional chromatographic separations.

47

There are two ways to combine two or more columns in mono-dimensional separations,

48

namely parallel and serial arrangements [7]. Serial columns generally outperform parallel

49

setups, as the resolution power is appreciably extended in this configuration. The effect of

50

changes in column length is different in the serial and parallel approaches. The serially

51

coupled columns approach has an intrinsic advantage: there is an additional separation

52

factor (the column length), which however has no consequence in the experimental effort. In

53

practice, each serial combination of short columns of different chemical nature and length

54

operates as a new column, with its own selectivity. This increases enormously the wealth of

55

columns available in a laboratory, from which the best one can be selected for a given

56

application [7].

57

In most cases, the aim of column coupling remains to increase the chromatographic

58

performance. The kinetic plot method (KPM) is often used as a design tool to find out the

59

optimal column length to achieve a given number of theoretical plates [8,9]. The KPM can be

60

used to predict the analysis time and efficiency which vary over a wide range of different

61

column lengths, from very short to very long columns. Although the length independence is

62

implicitly contained in the definition of the plate height concept, there are a number of cases

63

wherein deviations from this behavior can be expected (axial temperature gradient due to

64

viscous heating, extra-column band broadening effects which have relatively higher impact

65

on small columns, side-wall effects that persist along the column length, pressure-related

66

effects, etc.) [10,11,12,13]. The possibility to predict the performance of coupled columns

67

systems has been extensively studied in the past. Coupling of up to six columns (900 mm = 6

68

x 150 mm) showed that the KPM prediction was in good agreement with the obtained

69

(4)

4

performance on the coupled column system [14]. In another study [15], it has been

70

demonstrated that up to 8 columns (packed with 5 µm particles) could be coupled in series

71

and operated at a constant flow rate without any significant loss of efficiency, again implying

72

that the observed plate heights were independent on the column length.

73

The best combination of coupled columns in isocratic mode having different lengths and

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particle sizes was determined in a previous study from Cabooter et al. based on the Knox-

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Saleem speed limit [16]. Considering an ultrahigh-performance liquid chromatography

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(UHPLC) system operating at a pressure of 1200 bar, the best possible serial connection

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system can approach the 75–85 % of its Knox-Saleem limit whereas a three-column parallel

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system can only get about 50–60 % of the speed limit, while needing 50–100 % more total

79

column length. In absolute terms, the serially-connected system with individually optimized

80

segment lengths should be able to cover a range of 5000–75,000 theoretical plates in an

81

average analysis time of 14.3 min when using a 1200 bar instrument [16].

82

When working in gradient mode, the overall peak capacity can be predicted in a very similar

83

way on the basis of peak capacity measured on one single column, and assuming no

84

differences in the performance of columns that will be coupled in series. Peak capacity

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prediction has indeed shown very good accuracy when coupling four columns of 150 mm in

86

series [17]. Despite neglecting the possible variations in performance of the individual

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columns (different batches, history of the column), the kinetic performance limit approach

88

works well in practice, as long as chromatographers couple the same type of columns (same

89

stationary phase and dimension) in series.

90

Therefore, in isocratic mode the plate numbers are expected to be additive, while in gradient

91

mode, the peak capacity is proportional with the square root of the column length [18].

92

Serial column coupling can be useful for various types of applications and is particularly used

93

in RPLC mode [19]. By using a 450 mm long column (3 x 150 mm), the peak capacity of an

94

antibody peptide mapping analysis was increased up to nc = 704 [20]. The same concept has

95

also been used for intact and sub-units antibody analysis [20]. Another study showed the

96

possibilities to achieve high plate count and peak capacity at various combinations of column

97

(5)

5

lengths and temperatures [21]. Column coupling has also been applied in ion-exchange (IEX)

98

chromatography to improve the separation of intact antibody charge-variants [22]. In

99

supercritical fluid chromatography (SFC), 4 columns (4 x 100 mm) were successfully coupled

100

to increase the separation of 24 pharmaceutical compounds [23]. Column coupling can also

101

be applied for chiral separations [24]. As an example, an in-line coupling of achiral and chiral

102

columns was shown to be a good alternative to multidimensional chiral chromatography [24].

103

Coupling columns of different pore sizes in series is also commonly used in size exclusion

104

chromatography (SEC) to tune the selectivity of polymer separations [25].

105

Other purposes of column coupling can be post-column derivatization, on-line clean-up or the

106

protection of the analytical column by using guard (pre-) columns [26,27].

107

The purpose of this study was to estimate and measure the apparent efficiency of columns

108

made of identical stationary phase chemistry but possessing differences in their kinetic

109

performance. It may happen that the individual columns do not have identical efficiency

110

(different batch, different lifetime and antecedents, or different packing quality which is well-

111

known to be dependent on column length and diameter [28]). Different particle sizes were

112

used to mimic columns of different batches or columns providing different efficiencies when

113

coupling them in series. In isocratic mode, the plate numbers do not always seem additive

114

and kinetic performance has a limiting value, depending on the efficiency and length of the

115

individual columns. Furthermore, in gradient elution mode, the system is indifferent to the

116

column order. Theory has been developed to show the evolution of plate numbers for

117

coupling arbitrary several columns in isocratic mode and to predict peak widths for two

118

columns system in gradient mode. Experimental measurements have been performed to

119

validate the theory.

120 121

2. Theory

122

2.1 Peak widths in isocratic elution

123

The band dispersion in serially connected columns can be calculated by solving the following

124

ordinary differential equation:

125

(6)

6

(1)

126

where is the spatial variance of bands of compounds inside the column, the spatial

127

variable, and the height equivalent to a theoretical plate, HETP.

128

(2)

129

where and are the HETP and length of the ith column, respectively. Note that is

130

equal to zero.

131

The solution of Eq. (1) in case of sequentially connected columns with the initial condition

132

is:

133

(3)

134

Assuming that retention factors ( ) of solutes are the same in all the columns (identical

135

stationary phase chemistry), the retention time of a compound can be expressed as:

136

(4)

137

where is the hold-up time, and is the average linear velocity of the eluent in the ith

138

column.

139

By matching the spatial (σz) and time (σ) variances through the definition of efficiency and

140

replacing tR by Eq. (4), the following is obtained for a chromatographic peak eluted from

141

sequentially connected columns is:

142

(5)

143

The fraction on the right hand side of Eq. (5) can be expressed from Eq. (4) as:

144

(6)

145

where Ln and are the length and dead volume of the last segment, is the total dead

146

volume of the sequentially connected columns. Explicitly, with and are

147

the internal diameter and total porosity of column .

148

(7)

7

Eq. (6) can be combined with Eq. (5) and the peak width can be calculated as:

149

(7)

150

where,

151

(8)

152

The total plate number of the sequentially connected columns is the sum of the number of

153

theoretical plates of the columns. The apparent plate number, however, can be calculated

154

155

as:

(9)

156

Eqs. (8) and (9) can be generalized after the following considerations:

157

, ,

(10)

158

Accordingly,

159

(11)

160

and,

161

(12)

162

The ratio of and the total plate number is:

163

(13)

164

For a two-column system Eqs. (11), (12) and (13) become:

165

(14)

166

(15)

167

(16)

168

(8)

8

There are also several specific situations for two-columns:

169

If the plate numbers of the two columns are equal:

170

(17)

171

If the column diameters are equal:

172

(18)

173

If the column diameters and lengths are equal:

174

(19)

175

If the plate numbers and diameters of the two columns are equal:

176

(20)

177

If the efficiency of one of the two columns is infinite (N2= ∞)

178

(21)

179

If the efficiency of one of the two columns is infinite (N2= ∞)) and the column dimensions are

180

identical:

181

(22)

182

Peak capacity, , can be obtained as the solution of the following ordinary differential

183

equation with the initial condition of :

184

(23)

185

where is peak width as a function of time, .

186

The peak capacity of a series of columns connected together in isocratic mode can then be

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calculated as the solution of Eq. (23):

188

(24)

189

For a two-columns system, the following equation can be written:

190

(9)

9

(25)

191

If the column dimensions are identical and one of the columns has an infinite efficiency (N2 =

192

193

∞):

(26)

194

195

2.2 Peak widths in gradient elution

196

In gradient chromatography, the arrival time of a peak to a position z along the column is no

197

longer just proportional to time, but has to be retrieved from solving a differential equation,

198

given by:

199

(27)

200

where the velocity u is given by the instantaneous linear velocity of the solute, related to that

201

of the mobile phase (u0) through the solute retention (k):

202

(28)

203

Notice that the condition implies a negligible dwell volume. This is always the case

204

for initially highly retained compounds, that are stopped at the head of the column until the

205

gradient releases them. According to the linear solvent strength (LSS) theory, the retention

206

factor can be written as a function of the mobile phase composition [29]:

207

(29)

208

where S is the slope of the LSS model (log k vs. % organic modifier) and kw is the

209

extrapolated value of k for a compound eluted with pure A eluent (i.e., Φ=0). When running a

210

linear gradient over a time the mobile phase composition at the inlet of the column is given

211

by:

212

(30)

213

The retention at a time t and position z, taking into account the time it takes for the

214

mobile phase to reach that point, will be (again neglecting the dwell volume):

215

(10)

10

(31)

216

where is the initial retention, L the length of the column, t0 = L/u0 the hold-up

217

time, and:

218

(32)

219

Is the intrinsic gradient steepness.

220

The solution of (27) is the well-known chromatography formula:

221

(33)

222

The time to travel to z = L is the retention time, expressed as:

223

(34)

224

Peak width is mostly affected by diffusion and dispersion processes and by the gradient band

225

compression effect. The peak is compressed because of the changes to its trajectory while

226

crossing the gradient within the column. During gradient elution, the rear part of the peak

227

moves faster than its front part, because the mobile phase strength increases along the

228

column. The steeper the gradient, the higher the band compression effect is. To model the

229

band compression effect, it is useful to consider a peak between a point z and = z + .

230

Then the next formula can be written:

231

(35)

232

When w is small compared to the total length over which the motion of the peak is integrated,

233

the right-hand side of eq (35) can be expanded at first order in w to obtain:

234

(36)

235

Our goal is to have z as an independent variable, so with the chain rule, the following

236

equation can be obtained:

237

(37)

238

The speed gradient at a given position is obtained by plugging in the solution the equation

239

(33):

240

(11)

11

(38)

241

where,

242

(39)

243

is a measure of the gradient steepness. It takes into account that initially unretained

244

substances (k0 = 0) will not be compressed at all.

245

The band broadening effects can be dependent on the column HETP measured in isocratic

246

mode, which we call here H0,

247

(40)

248

Equation (40) can be joined with (37) to give:

249

(41)

250

If the width at a given point along the column z0 (this will be necessary for the coupling)

251

is known:

252

(42)

253

the solution is:

254

(42)

255

By neglecting the initial peak width caused by the injection process, when z = 0, we

256

obtain the known formula at elution (z = L):

257

(43)

258

We now assume a two-column system possessing different HETP values, H1 for length L1,

259

and H2 for length L2. If the same gradient steepness and linear velocity are considered on the

260

two columns, then the migration can still be described by equation (33), with L = L1 + L2. In

261

the first column, the width evolves from the injection width at z = 0. By setting H0 = H1,

262

= and z0 = 0 in equation (42), the following equation can be obtained:

263

(12)

12

(44)

264

When it reaches z = L1, it starts migrating under H2. The coupling condition is:

265

(45)

266

This means that follows equation (42), with H0 = H2, z0 = L1 and = (L1), thus

267

defining:

268

(46)

269

the solution becomes:

270

(47)

271

or over the whole coupled system:

272

(48)

273

The result is very similar to (44), with a correction factor proportional to . At elution, z = L =

274

L1 + L2 :

275

(49)

276

Please note that the dependence in H1 only comes through . In particular, if L1 is smaller

277

than L, then the efficiency is basically dominated by the second column.

278 279

3. Experimental

280

3.1 Chemicals and columns

281

Acetonitrile, methanol and ethanol (gradient grade) were purchased from Sigma-Aldrich

282

(Buchs, Switzerland). Water was obtained with a Milli-Q Purification System from Millipore

283

(Bedford, MA, USA).

284

Uracil, methylparaben, ethylparaben, propylparaben, butylparaben, cannabidivarine (CBDV),

285

cannabigerolic acid (CBGA), tetrahydrocannabivarin (THCV), cannabichromene (CBC),

286

delta9-tetrahydrocannabinolic acid (THCA-A) and human serum albumin (HSA), were

287

(13)

13

purchased from Sigma–Aldrich. Cannabidiolic acid (CBDA), cannabigerol (CBG), cannabidiol

288

(CBD), cannabinol (CBN), (-)-delta9-THC (d9-THC) and (-)-delta8-THC (d8-THC) were

289

purchased from Lipomed AG (Arlesheim, Switzerland).

290

Ammonium hydroxide solution, formic acid (FA), trifluoroacetic acid (TFA), dithiothreitol

291

(DTT) and trypsin were obtained from Sigma-Aldrich.

292

X-Bridge C18 (5 µm, 150 x 4.6 mm) (A), X-Bridge C18 (3.5 µm, 100 x 4.6 mm) (B) and X-

293

Bridge C18 (2.5 µm, 75 x 4.6 mm) (C) columns were purchased from Waters (Milford, MA,

294

USA). Jupiter C18 (5 µm 300 Å, 150 x 2.0 mm) (D) and Jupiter C18 (3 µm 300 Å, 150 x 2.0

295

mm) (E) columns were purchased from Phenomenex (Torrance, CA, USA).

296 297

3.2 Equipment and software

298

The measurements were performed using a Waters Acquity UPLCTM I-Class system

299

equipped with a binary solvent delivery pump, an autosampler and UV detector and/or

300

fluorescence detector (FL). The system includes a flow through needle (FTN) injection

301

system equipped with 15 µL needle, a 0.5 µL UV flow-cell and a 2 µL FL flowcell. The

302

connection tube between the injector and column inlet was 0.003” I.D. and 200 mm long

303

(active preheating included), and the capillary located between the column and detector was

304

0.004” I.D. and 200 mm long. The overall extra-column volume (Vext) was about 8.5 µL and

305

11 µL as measured from the injection seat of the auto-sampler to the detector cell (UV and

306

FL, respectively). The average extra-column peak variance of our system was found to be

307

around ∼0.5 − 3 µL2 (depending on the flow rate, injected volume, mobile phase

308

composition and solute). Data acquisition and instrument control were performed by

309

Empower Pro 3 Software (Waters).

310 311

3.3 Chromatographic conditions and sample preparation

312

3.3.1. Apparent plate numbers: Isocratic measurements of parabens and uracil

313

(14)

14

A mix solution containing uracil, methylparaben, ethylparaben, propylparaben and

314

butylparaben was prepared in 80 : 20 v/v water : acetonitrile at 50 µg/mL.

315

For isocratic chromatographic measurements, the mobile phase was composed of 55 : 45 v/v

316

water : acetonitrile. Experiments were performed at a flow rate of 1 mL/min at ambient

317

temperature. Detection was carried out at 254 nm (40 Hz), the injection volume was 5 µL.

318

The plate numbers were measured on three single columns, namely the 5 µm, 150 x 4.6 mm

319

(A), 3.5 µm, 100 x 4.6 mm (B) and 2.5 µm, 75 x 4.6 mm (C) columns, then the columns were

320

coupled in series using 5 cm long (0.175 mm ID) stainless steel tubing and the apparent

321

plate numbers were measured. The following combinations were tested: (1) columns A + B,

322

(2) columns A + C, (3) columns B + C and (4) columns A + B + C.

323 324

3.3.2. Apparent peak widths: gradient measurements of small molecules (mix of

325

cannabinoids)

326

A mix solution containing eleven cannabinoids (i.e. CBDV, CBGA, THCV, CBC, THCA-A,

327

CBDA, CBG, CBD, CBN, d9-THC and d8-THC) was prepared from individual stock solutions

328

diluted in solvent having the same composition as the initial mobile phase (55 : 45 v/v 10 mM

329

ammonium-acetate : acetonitrile) at 90 µg/mL. The individual stock solutions were prepared

330

in either methanol, acetonitrile or ethanol depending on their solubility. Mobile phase “A” was

331

10 mM ammonium-acetate (pH = 5.8), mobile phase “B” was acetonitrile. Linear gradients

332

were run from 45 %B to 100 %B at 1 mL/min flow rate and ambient temperature. The

333

gradient time (tG) over column length (L) ratio was kept constant (tG/L=1 min/cm) when

334

running gradients on different column lengths (corresponds to e.g. tG = 10 min on 10 cm long

335

column). Detection was carried out at 220 and 254 nm (40 Hz), the injection volume was 10

336

µL. The peak widths (peak capacity) were measured on three single columns, namely on the

337

5 µm, 150 x 4.6 mm (A), 3.5 µm, 100 x 4.6 mm (B) and 2.5 µm, 75 x 4.6 mm (C) columns,

338

and then these columns were coupled in series using 5 cm long (0.175 mm ID) stainless

339

steel tubing, and the apparent peak widths (peak capacity) were measured. The following

340

(15)

15

combinations were used: (1) columns A + B, (2) columns A + C, (3) columns B + C and (4)

341

columns A + B + C.

342 343

3.3.3. Apparent peak widths: gradient measurements of peptides (HSA tryptic digest)

344

Tryptic digestion of human serum albumin (HSA) was carried out as described in a recent

345

protocol [30]. Mobile phase “A” was 0.1 % TFA in water, mobile phase “B” was 0.1 % TFA in

346

acetonitrile. Linear gradients were run from 10 to 70 %B at a flow rate of 0.3 mL/min and 50

347

˚C. The gradient time (tG) over column length (L) ratio was kept constant (tG/L=2 min/cm)

348

when running gradients on different column lengths (corresponds to e.g. tG = 30 min on 15

349

cm long column). Fluorescence detection was carried out at 280 nm as excitation and 350

350

nm as emission wavelengths, the injection volume was 5 µL. The peak widths (peak

351

capacity) were measured on two widepore columns of 5 µm, 150 x 2.0 mm (D) and 3 µm,

352

150 x 2.0 mm (E) columns, then these two columns were coupled in series using 5 cm long

353

(0.175 mm ID) stainless steel tubing, and the apparent peak widths (peak capacity) were

354

measured. The following combinations were used: (1) columns D + E and (2) columns E + D.

355 356

4. Results and Discussion

357

4.1. Apparent plate number in isocratic mode for serially coupled columns

358

As it is possible to couple together two columns possessing different lengths and efficiencies,

359

an informative representation of the apparent plate number (Napp) can be obtained when

360

plotting the ratio of Napp/Nsum (where Nsum is the sum of the individual plate counts) as a

361

function of N1/N2 (corresponding to the efficiency of the first and second columns,

362

respectively). In this type of representation, various ratios of column lengths (L1/L2) can be

363

tested. Figure 1 shows some plots for L1/L2 = 0.75, 1, 1.5 and 2 (calculations are based on

364

eq 18). As suggested by the theory, all the curves show a maxima (Napp/Nsum = 1), indicating

365

that the highest reachable efficiency with two serially coupled columns is equal to the sum of

366

the individual plate numbers. However, it only occurs at a given ratio of column lengths.

367

When coupling two columns of identical lengths (L1/L2 = 1) in series, then this maximum

368

(16)

16

occurs when the columns possess identical plate numbers (N1/N2 = 1). When the first column

369

is twice longer than the second one (L1/L2 = 2), then the maximum plate number is attained

370

when the first column performs twice as high plate numbers than the second one (N1/N2 = 2).

371

Similarly, when L1/L2 = 1.5 and 0.75, the maximum performance is expected for N1/N2 = 1.5

372

and 0.75, respectively. Accordingly, to obtain the maximum efficiency from equal coupled

373

columns configuration, it is required that their plate heights should be the same. In this case,

374

the apparent plate count is the sum of the individual plate counts. In any other case,

375

Napp/Nsum will be smaller than 1. An important feature of the system is its symmetric property,

376

meaning that the system (or N) is indifferent to the order. One can choose the more efficient

377

column either in the first or the second position, without affecting the global efficiency.

378

Table 1 shows the measured and calculated plate numbers on single columns (A, B and C)

379

and serially coupled configurations (including two and three columns) for four model

380

compounds (parabens). As shown, the measured and predicted plate numbers are in very

381

good agreement, with a variation between measured and predicted efficiency comprised

382

between -7 and +5 %. Figure 1 also includes the experimentally measured values which fit

383

quite well with the theoretical curves. As an example, Figure 2 shows some representative

384

chromatograms of the four parabens separated on three different columns with different

385

lengths and efficiency as well as with the three columns serially coupled.

386

Another interesting aspect is to track the efficiency increase of two serially coupled columns

387

compared to just one of the columns used for this coupling. Figure 3 illustrates Napp/N1 as a

388

function of N1/N2 for three cases, namely for L1/L2 = 0.2, 1 and 2 with identical column

389

diameters. When L1/L2 = 2 (the first column is twice as long as the second one), the intercept

390

of the curve corresponds to Napp/N1 = 2.25. This means that the maximum efficiency is 2.25

391

times higher vs. that of the first column. It occurs when the second column has infinite

392

efficiency (intercept at N1/N2=0). In this case, the second column only increases retention

393

times without any effect on band broadening. As illustrated in Figure 3, it is not possible to

394

attain higher plate numbers with this setup. On the other hand, if the efficiency of the second

395

column is five times lower than that of the first column, then the apparent plate number of

396

(17)

17

serially coupled columns will be the same as of the first column. When N1/N2 is above 5, the

397

overall efficiency of the coupled system is lower than the efficiency of the first column. This

398

means that it is possible to combine two HPLC columns that finally generate lower resolution

399

than that offered by the most efficient column alone. This counter instinctive consequence is

400

analogous to the band broadening effect due to the extra column contributions. Similarly,

401

when L1/L2 = 1, the maximum achievable efficiency is four times higher than that of the first

402

column, while if the efficiency of the second column is at least three times lower than the first

403

column, then no increase in efficiency is obtained when coupling these two columns. Finally,

404

when the first column is very short compared to the second column (L1/L2 = 0.2) and the

405

second column has very high efficiency (infinite) then Napp/N1 = 36 can be attained when

406

coupling the columns.

407

In general, when efficiency of the second column is infinite, the apparent plate number of the

408

two-column system becomes:

409

(50)

410

The condition when additional gain of efficiency can be obtained by coupling two columns is:

411

(51)

412

or similarly,

413

(52)

414

where , , and .

415

Accordingly, additional gain of efficiency and resolution is possible by coupling two HPLC

416

columns only if the column plate heights do not differ too significantly.

417 418

4.2. The evolution of peak width and peak capacity in gradient mode for serially coupled

419

columns

420

In gradient elution mode, the order of the columns is concerned, and the observed apparent

421

efficiency strongly depends on the order of the columns (non-symmetrical system). An

422

illustration is given in Figure 4. Assuming two columns (with the same internal diameter) with

423

(18)

18

plate heights, H = 10 μm and H = 40 μm, respectively coupled in series. The peak width will

424

evolve in different ways depending on the column order and length of the individual

425

segments (the different plate heights were assumed to mimic columns of different batches or

426

the combination of old and new columns). The continuous lines in Figure 4 show the peak

427

widths for coupled columns possessing different efficiencies as a function of the position of

428

the solute (z) along its travel. The dashed lines correspond to columns having either H = 10

429

μm or H = 40 μm efficiency along its entire length (10 cm) – as reference values.

430

Figure 4A shows the case where two segments of 5 cm are coupled at a moderate gradient

431

steepness (p=1). When placing the more efficient column in the first position and the less

432

efficient one in the second position (continuous red line) – as expected – the peak will

433

broaden drastically after entering the second (less efficient) column as the band broadening

434

caused by dispersion and diffusion processes becomes more important. However, when

435

having the less performing column in the first position and the most efficient column in the

436

second position (continuous blue line), interestingly the peak width will decrease

437

continuously during the travel of the solute along the second column (“peak sharpening”). It

438

suggests that the gradient band compression effect outperforms the dispersive and diffusive

439

effects in the second column as the more efficient column offers much lower H value than the

440

first column. If the second - more efficient - column is very long compared to the first one, the

441

peak width will approach the limiting value theoretically obtained only with the more efficient

442

column - indeed, the dashed line (single column with maximal efficiency) is an asymptote of

443

the solid line (coupled system), that are equal in the large z limit.

444

Figure 4B represents a situation where the column lengths are different. The first one is four

445

times shorter than the second one. When placing the better column in the first position, then

446

a trend similar to that of Figure 4A can be seen. However the coupled system approaches

447

faster its limit (see the dashed and continuous red lines) because at the beginning of the

448

solute’s travel along the column, the gradient compression effect is stronger than later during

449

the travel (e.q. 38). When putting the more efficient column as the second one, then no band

450

broadening occurs in the second column, and the peak width remains more or less constant

451

(19)

19

whilst the solute is traveling through the second column (continuous blue line). It suggests

452

that the gradient band compression effect nearly compensates the band broadening caused

453

by dispersion and diffusion processes. Please note that the differences between the coupled

454

systems – with columns possessing different efficiencies - were larger in this case compared

455

to the situation where the lengths were identical (see the differences at z = 10 cm between

456

the continuous blue and red lines in Figures 4A and 4B).

457

Finally, figure 4C corresponds to a situation with two columns of 5 cm – similarly to Figure 4A

458

– but for a steeper gradient (p = 10). The trends were similar as the ones observed in Figure

459

4A, but as expected the gradient focusing effect was more important, and therefore the total

460

peak width was smaller. When placing the better column in the second position (continuous

461

blue line), the speed of peak compression was faster on the second column compared to the

462

case where a flatter gradient was applied.

463

To verify the theory developed for predicting the peak width in gradient mode, two sets of

464

compounds were analyzed using serially connected columns having different particle sizes

465

and lengths. Figure 5 shows the separations of 11 cannabinoids on three different individual

466

columns and on different combinations of two or three columns, as selected examples. Table

467

1 contains the experimentally measured and predicted peak widths for the first and last

468

eluting peaks. The peak width prediction for serially coupled columns was based on the peak

469

widths measured on the individual columns. In particular, values for single column

470

efficiencies were retrieved from direct measurements of peak width. These efficiencies were

471

then used as the input for the coupled formula (e.q. 49). The measured and calculated widths

472

were in very good agreement, as the average error in prediction was about 5-6 %.

473

Another experimental verification was performed by injecting HSA tryptic digest on two

474

individual widepore columns packed with 5 and 3 μm particles and on the combination of

475

these two columns in different orders (Figure 6). Larger molecules (peptides) possess higher

476

S values, therefore it was interesting to check the validity of the model calculations for such

477

molecules. The peak widths of the three most intense (and well separated) peaks was

478

predicted for the coupled systems from the widths on the single columns. Again, very good

479

(20)

20

agreement was found between experimentally observed and calculated peak widths (Table

480

3), as the average error in prediction was about 6 %. The results confirm the importance of

481

the columns order as the order “D + E” always gave thinner peaks than “E + D” (both for

482

predicted and measured peak widths).

483 484

5. Conclusions

485

The serially coupled columns approach has an intrinsic advantage as it offers an additional

486

separation factor (the column length). In most cases, the column length is increased by

487

coupling columns packed with the same material (i.e. stationary phase and particle size). In

488

this case, the plate number observed with the coupled column system is the sum of the plate

489

counts observed on the individual column segments. However, it may happen that the

490

individual columns do not have identical efficiency (different batch, different lifetime and

491

antecedents, or different packing quality which is well-known to be dependent on column

492

length and diameter). Therefore, coupling columns with different efficiencies in series raises

493

some questions: (1) What will be the final apparent efficiency?, (2) What is the maximum

494

efficiency that can be reached?, and (3) Does the column order play a significant role?

495

Theory was developed for both isocratic and gradient modes, to predict the peak widths for

496

coupled column systems. In isocratic mode, the plate numbers are not additive anymore

497

when the columns possess different plate count, and kinetic performance has a limiting value

498

which depends on the efficiency and length of the individual columns.

499

Furthermore, in gradient elution mode, the order of the columns is not indifferent. Indeed, the

500

observed apparent efficiency significantly depends on the column order (non-symmetrical

501

system). In combinations, when the latter column has higher efficiency, a decrease of the

502

peak width is predicted (“peak sharpening”), when the solute travels this segment. This

503

means that the gradient band compression effect compensates and outperforms the

504

competing band broadening caused by dispersive and diffusive processes. Therefore, the

505

columns should be placed in order of increasing efficiency.

506

(21)

21

Experimental measurements have been performed in both isocratic and gradient modes to

507

verify the developed theory. Very good agreement was found between measured and

508

calculated peak widths.

509

To conclude for serially coupled column systems in gradient mode, besides the total length of

510

the coupled column, additional important factors are the order and lengths of the individual

511

segments which must be considered when optimizing a gradient separation.

512 513

6. Acknowledgements

514

The authors wish to thank Jean-Luc Veuthey and Balazs Bobaly from the University of

515

Geneva for fruitful discussions.

516

Davy Guillarme wishes to thank the Swiss National Science Foundation for support through a

517

fellowship to Szabolcs Fekete (31003A 159494).

518

Krisztián Horváth acknowledges the financial support of the Hungarian Government and the

519

European Union, with the co-funding of the European Social Fund in the frame of GINOP

520

Programme [Code No: GINOP-2.3.2-15-2016-00016], and of the János Bolyai Research

521

Scholarship of the Hungarian Academy of Sciences.

522

(22)

22

References

523

[1] J.L. Glajch, J.C. Gluckman, J.G. Charikofsky, J.M. Minor, J.J. Kirkland, Simultaneous

524

selectivity optimization of mobile and stationary phases in RPLC for isocratic separations of

525

phenylthiohydantoin amino acid derivatives, J. Chromatogr. 318 (1985) 23–39.

526

[2] P.H. Lukulay, V.L. McGuffin, Solvent modulation in liquid chromatography: extension to

527

serially coupled columns, J. Chromatogr. A 691 (1995) 171–185.

528

[3] F. Garay, Application of a flow-tunable, serially coupled gas chromatographic capillary

529

column system for the analysis of complex mixtures, Chromatographia 51 (2000) 108–120.

530

[4] Sz. Nyiredy, Z. Szücs, L. Szepesy, Stationary phase optimized selectivity liquid

531

chromatography: Basic possibilities of serially connected columns using the PRISMA

532

principle, J. Chromatogr.A 1157 (2007) 122–130.

533

[5] K. Chen, F. Lynen, M. De Beer, L. Hitzel, P. Ferguson, M. Hanna-Brown, P. Sandra,

534

Selectivity optimization in green chromatography by gradient stationary phase optimized

535

selectivity liquid chromatography, J. Chromatogr. A 1217 (2010) 7222-7230.

536

[6] T. Alvarez-Segura, J.R. Torres-Lapasio, C. Ortiz-Bolsico, M.C. García-Alvarez-Coque,

537

Stationary phase modulation in liquid chromatography through the serial coupling of

538

columns: A review, Anal. Chim. Acta, 923 (2016) 1-23.

539

[7] T. Alvarez-Segura, C. Ortiz-Bolsico, J.R. Torres-Lapasio, M.C. Garcia-Alvarez-Coque,

540

Serial versus parallel columns using isocratic elution: A comparison of multi-column

541

approaches in mono-dimensional liquid chromatography, J. Chromatogr. A 1390 (2015) 95–

542

102.

543

[8] G. Desmet, D. Clicq, P. Gzil, Geometry-independent plate height representation methods

544

for the direct comparison of the kinetic performance of LC supports with a different size or

545

morphology, Anal. Chem. 77 (2005) 4058-4070.

546

[9] D. Cabooter, F. Lestremau, F. Lynen, P. Sandra, G. Desmet, Kinetic plot method as a tool

547

to design coupled column systems producing 100,000 theoretical plates in the shortest

548

possible time, J. Chromatogr. A 1212 (2008) 23–24.

549

(23)

23

[10] U.D. Neue, M. Kele, Performance of idealized column structures under high pressure, J.

550

Chromatogr. A 1149 (2007) 236-244.

551

[11] W.Th. Kok, U.A.Th. Brinkman, R.W. Frei, H.B. Hanekamp, F. Nooitgedacht, H. Poppe,

552

Use of conventinal instrumentation with microbore column in high-performance liquid

553

chromatography, J. Chromatogr. 237 (1982) 357-369.

554

[12] K. Broeckhoven, G. Desmet, Approximate transient and long time limit solutions for the

555

band broadening induced by the thin sidewall-layer in liquid chromatography columns, J.

556

Chromatogr. A 1172 (2007) 25-39.

557

[13] S. Fekete, K. Horvath, D. Guillarme, Influence of pressure and temperature on molar

558

volume and retention properties of peptides in ultra-high pressure liquid chromatography, J.

559

Chromatogr. A 1311 (2013) 65-71.

560

[14] F. Lestremau, A. de Villiers, F. Lynen, A. Cooper, R. Szucs, P. Sandra, High efficiency

561

liquid chromatography on conventional columns and instrumentation by using temperature as

562

a variable: Kinetic plots and experimental verification, J. Chromatogr. A 1138 (2007) 120-

563

131.

564

[15] F. Lestremau, A. Cooper,R. Szucs, F. David, P. Sandra, High-efficiency liquid

565

chromatography on conventional columns and instrumentation by using temperature as a

566

variable: I. Experiments with 25 cm × 4.6 mm I.D., 5 μm ODS columns, J. Chromatogr. A

567

1109 (2006) 191-196.

568

[16] D. Cabooter, G. Desmet, Performance limits and kinetic optimization of parallel and

569

serially connected multi-column systems spanning a wide range of efficiencies for liquid

570

chromatography, J. Chromatogr. A 1219 (2012) 114-127.

571

[17] A. Vaast, J. De Vos, K. Broeckhoven, M. Verstraeten, S. Eeltink, G. Desmet, Maximizing

572

the peak capacity using coupled columns packed with 2.6 µm core–shell particles operated

573

at 1200 bar, J. Chromatogr. A 1256 (2012) 72-79.

574

[18] U.D. Neue, Peak capacity in unidimensional chromatography, J. Chromatogr. A 1184

575

(2008) 107-130.

576

(24)

24

[19] S. Fekete, J.L. Veuthey, D. Guillarme, Comparison of the most recent chromatographic

577

approaches applied for fast and high resolution separations: Theory and practice, J.

578

Chromatogr. A 1408 (2015) 1-14.

579

[20] S. Fekete, M.W. Dong, T. Zhang, D. Guillarme, High resolution reversed phase analysis

580

of recombinant monoclonal antibodies by ultra-high pressure liquid chromatography column

581

coupling, J. Pharm. Biomed. Anal. 83 (2013) 273-278.

582

[21] D. Guillarme, E. Grata, G. Glauser, J.L. Wolfender, J.L. Veuthey, S. Rudaz, Some

583

solutions to obtain very efficient separations in isocratic and gradient modes using small

584

particles size and ultra-high pressure, J. Chromatogr. A 1216 (2009) 3232-3243.

585

[22] S. Fekete, A. Beck, D. Guillarme, Characterization of cation exchanger stationary

586

phases applied for the separations of therapeutic monoclonal antibodies, J. Pharm. Biomed.

587

Anal. 111 (2015) 169-176.

588

[23] A.G.G. Perrenoud, C. Hamman, M. Goel, J.L. Veuthey, D. Guillarme, S. Fekete,

589

Maximizing kinetic performance in supercritical fluid chromatography using state-of-the-art

590

instruments, J. Chromatogr. A 1314 (2013) 288-297.

591

[24] N.C.P. Albuquerque, J.V. Matos, A.R.M. Oliveira, In-line coupling of an achiral-chiral

592

column to investigate the enantioselective in vitro metabolism of the pesticide Fenamiphos

593

by human liver microsomes, J. Chromatogr. A 1467 (2016) 326-334.

594

[25] R. Eksteen, H.G. Barth, B. Kempf, The effect of sec column arrangement of different

595

pore sizes on resolution and molecular weight measurements, LCGC North America, 29

596

(2011) 668–671.

597

[26] A. Jones, S. Pravadali-Cekic, G.R. Dennis, R.A. Shalliker, Post column derivatisation

598

analyses review. Is post-column derivatisation incompatible with modern HPLC columns?,

599

Anal. Chim. Acta, 889 (2015) 58-70.

600

[27] M. Javanbakht, M.M. Moein, B. Akbari-adergani, On-line clean-up and determination of

601

tramadol in human plasma and urine samples using molecularly imprinted monolithic column

602

coupling with HPLC, J. Chromatogr. B, 911 (2012) 49-54.

603

(25)

25

[28] S. Schweiger, S. Hinterberger, A. Jungbauer, Column-to-column packing variation of

604

disposable pre-packed columns for protein chromatography, J. Chromatogr. A, 1527 (2017)

605

70-79.

606

[29] L.R. Snyder, J.W. Dolan, High-performance gradient elution: The practical application of

607

the linear solvent strength model, John Wiley & Sons, Inc. 2007

608

[30] B. Bobaly, V. D’Atri, A. Goyon, O. Colas, A. Beck, S. Fekete, D. Guillarme, Protocols for

609

the analytical characterization of therapeutic monoclonal antibodies. II – Enzymatic and

610

chemical sample preparation, J. Chromatogr. B 1060 (2017) 325-335.

611

612

613

(26)

26

Table 1.

614 615

column L (mm)

N

methylparaben ethylparaben propylparaben butylparaben measured predicted measured predicte

d measured predicted measured predicted

A 150 15111 - 14911 - 14763 - 15070 -

B 100 6066 - 6329 - 6512 - 6889 -

C 75 11509 - 12046 - 12478 - 12681 -

A+B 250 19388 19920 19792 20233 19863 20427 20956 21225

A+C 225 24744 25598 24955 25621 25599 25635 25902 26414

B+C 175 14406 14329 15301 14961 15921 15417 16440 16160

A+B+C 325 27857 29128 28757 29704 29256 30088 30690 31174

616

(27)

27

Table 2.

617 618

column L (mm)

peak 1 peak 11

w1/2

measured (min)

w1/2

predicted (min)

w1/2

measured (min)

w1/2

predicted (min)

Rs crit 9.10 peak capacity

A 150 0.0571 - 0.0715 - 0.69 134

B 100 0.0666 - 0.0771 - 0.55 83

C 75 0.0375 - 0.0399 - 0.57 119

B+A 250 0.0909 0.0993 0.1031 0.1162 0.88 144

C+A 225 0.075 0.0698 0.0838 0.0870 0.99 159

C+B 175 0.0852 0.0861 0.0964 0.0994 0.57 110

A+B+C 325 0.1054 0.0957 0.1098 0.1084 1.00 167

619

620

(28)

28

Table 3.

621 622

column L (mm)

peak 1 peak 2 peak 3

w1/2

measured (min)

w1/2

predicted (min)

w1/2

measured (min)

w1/2

predicted (min)

w1/2

measured (min)

w1/2

predicted (min)

peak capacity

D 150 0.0697 - 0.0703 - 0.0781 - 240

E 150 0.0592 - 0.0559 - 0.0525 - 312

D + E 300 0.0918 0.0857 0.0849 0.0819 0.088 0.0797 388

E + D 300 0.0923 0.0968 0.095 0.0971 0.0966 0.1066 362

623

624

(29)

29

Figure captions

625 626

Figure 1. Napp/Nsum (relative apparent efficiency of the coupled system) as a function of N1/N2

627

(ratio of individual column efficiency) for various column length ratios (L1/L2 = 0.75, 1, 1.5 and

628

2).

629 630

Figure 2. Experimentally obtained chromatograms of a mixture of uracil and 4 parabens on

631

columns A, B and C and on serially connected columns A+B+C in isocratic mode. The

632

mobile phase was composed of 55 : 45 v/v water : acetonitrile. Experiments were performed

633

at a flow rate of 1 mL/min at ambient temperature. Detection was carried out at 254 nm (40

634

Hz), the injection volume was 5 µL. Peaks: uracil (t0), methylparaben (1), ethylparaben (2),

635

propylparaben (3) and butylparaben (4).

636 637

Figure 3. Napp/N1 (apparent efficiency compared to the first column) as a function of N1/N2

638

(ratio of individual column efficiency) for various column length ratios (L1/L2 = 0.2, 1, and 2).

639 640

Figure 4. The evolution of peak variance ( along the column (z) for a system composed of

641

two columns coupled in series. Three cases named A to C are reported, corresponding to

642

different segment lengths and gradient steepness, considering H = 10 µm and 40 μm. Please

643

note that time based peak width as a practical measure of band broadening can be obtained

644

at the total length by .

645

646

Figure 5. Experimental chromatograms of cannabinoids mixture on columns A, B and C and

647

on serially connected combinations in gradient mode. Linear gradients were run from 45 to

648

100 %B at 1 mL/min and ambient temperature. The gradient time (tG) over column length (L)

649

ratio was kept constant (tG/L=1 min/cm) when running gradients on different column lengths.

650

Detection was carried out at 254 nm (40 Hz), and injection volume was 10 µL.

651 652

Figure 6. Experimental chromatograms of HSA tryptic digest on columns D and E and on

653

serially connected “D+E” and “E+D” combinations in gradient mode. Linear gradients were

654

run from 10 to 70 %B at 0.3 mL/min and 50 ˚C. The gradient time (tG) over column length (L)

655

ratio was kept constant (tG/L=2 min/cm) when running gradients on different column lengths.

656

Detection was carried out at 280 nm as fluorescence excitation and 350 nm as fluorescence

657

emission wavelengths, and injection volume was 5 µL.

658

659

660

(30)

30

Table captions

661 662

Table 1. Measured and predicted plate numbers for parabens in isocratic mode on three

663

individual columns and on their different combinations. (Predictions are based on eq. 18 for

664

two columns and 12 for three columns.)

665

666

Table 2. Measured and predicted peak widths for cannabinoids in gradient elution mode on

667

three individual columns and on their different combinations. The obtained critical resolution

668

and peak capacity are also shown. (Predictions are based on eq. 47-49.)

669

670

Table 3. Measured and predicted peak widths for peptides obtained in gradient elution mode

671

on two individual columns and on their combinations. The obtained peak capacity is also

672

indicated. (Predictions are based on eq. 47-49.)

673

674

(31)

Figure 1

Figure

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